In this work we introduce a new numerical approach for solving
Cahn-Hilliard equation with Neumann boundary conditions involving
recent mass transportation methods. The numerical scheme is based on
an alternative formulation of the problem using the so called
pseudo-inverse of the cumulative distribution function.
We establish a stable fully discrete scheme that inherits the
energy dissipation and mass conservation from the
associated continuous problem. We perform some numerical experiments
which confirm our results.